Electrophoresis is a technique widely used in biology to separate, classify, and study complex mixtures of macromolecules and particles (such as DNA). We have applied mathematical methods and techniques to problems in electrophoresis. In particular, we have developed models describing the motion of macromolecules and virus-sized particles in gels. We have defined a resolution function that is well adapted to electrophoretic separation of particles such as DNA. The models of motion, together with the resolution function, allow us to predict the minimal time and optimal migration path for the resolution of complex mixtures, such as those encountered in DNA sequencing. We have also developed methods for evaluating the efficiency of various polymers in the separation of macromolecules of various sizes. For this purpose, we have defined the separation efficiency function, as well as the resolution efficiency function. These functions are used to evaluate different polymers relative to one another. These techniques give us a practical means by which to select the most efficient sieving polymer solution for a particular molecular size. Finally, we have implemented the mathematical algorithms used in the analyses in a user-friendly software package for use on a personal computer.